Finite Group DatabasebetaFinite Group Databasebeta| order | 7308 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C32×C29⋊C7 |
| unambiguous semidirect product | (C22×C32×C29)⋊C7 |
| Fitting, socle, Hall | C22×C32×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C22×C32×C7 |
| Hall | C32×C29 ⋊ C22×C7 |
| Hall | C22×C29 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | C29⋊C7 |
| commutator, hypocenter | C29 | C22×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C32 | |
120 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C32×D5×C29⋊C7, C22×C32×C5×C29⋊C7 |
| maximal normal subgroup of | C22×C32×C5×C29⋊C7 |
| maximal quotient of | C2×C32×D5×C29⋊C7, C22×C32×C5×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7308, 109);